Skip to main content
SpringerLink
Log in

On universal approximation capability of fuzzy systems

  • Published:
Science in China Series E: Technological Sciences Aims and scope Submit manuscript

Abstract

The universal approximation capability of fuzzy systems using translations and dilations of one fixed function (called basis function) as their membership functions is discussed. Such types of fuzzy systems are proved to be universal approximators under conditions that the basis function is integrable, with nonvanishing integral, and a. e. continuous. This result enlarges the family of fuzzy systems which can be universal approximators. Two simulation experiments are designed to verify the conclusion.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Kosko, B., Fuzzy system as universal approximators,Proc. IEEE 1992 Int. Conf. Fuzzy Systems, Piscataway: IEEE Service Center, 1992, 1153–1162.

    Google Scholar 

  2. Wang, L. X., Mendel, J. M., Fuzzy basis functions, universal approximation, and orthogonal least-squares learning,IEEE Trans. Neural Networks, 1992, 3(5): 807.

    Article  Google Scholar 

  3. Zeng, X. J., Singh, M. G., Approximation theory of fuzzy systems—SISO case,IEEE Trans. Fuzzy Systems, 1994, 2 (2): 162.

    Article  Google Scholar 

  4. Zeng, X. J., Singh, M. G., Approximation theory of fuzzy systems—MIMO case,IEEE Trans. Fuzzy Systems, 1995, 3 (2): 219.

    Article  Google Scholar 

  5. Castro, J. L., Fuzzy logic controllers are universal approximators,IEEE Trans. Systems, Man, and Cybernetics, 1995, 25 (4): 629.

    Article  Google Scholar 

  6. Mao, Z. H., Li, Y. D., Zhang, X. F., Approximation capability of fuzzy systems using translations and dilations of one fixed function as membership functions,IEEE Trans. Fuzzy Systems, 1997, 5(3): 468.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Automation, Tsinghua University, 100084, Beijing, China

    Zhihong Mao, Xuefeng Zhang & Yanda Li

Authors
  1. Zhihong Mao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xuefeng Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yanda Li
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Mao, Z., Zhang, X. & Li, Y. On universal approximation capability of fuzzy systems. Sci. China Ser. E-Technol. Sci. 41, 6–12 (1998). https://doi.org/10.1007/BF02916866

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02916866

Keywords

Search

Navigation